March 2008
Imperfect Enforcement of Emissions Trading and Industry Welfare: A
Laboratory Investigation
John K. Stranlund
Department of Resource Economics
University of Massachusetts, Amherst
James J. Murphy ∗
Department of Economics
University of Alaska Anchorage
John M. Spraggon
Department of Resource Economics
University of Massachusetts, Amherst
Acknowledgements: Primary funding for this research was provided by the U.S. EPA – Science
to Achieve Results (STAR) Program grant #R829608. Additional support was provided by the
Cooperative State Research Extension, Education Service, U. S. Department of Agriculture,
Massachusetts Agricultural Experiment Station, and the Department of Resource
Economics under Project No. MAS00871, and by the Center for Public Policy and
Administration, University of Massachusetts-Amherst. Maria Alejandra Velez, Carrie Puglisi
and Maria Claudia Lopez provided outstanding research assistance. Glenn Caffery programmed
the software for this project. Wendy Varner provided valuable administrative support. The
authors take full responsibility for any errors or omissions. The authors acknowledge helpful
comments by participants in the Seminar in Environmental Economics and Policy at Harvard
University, and at Advanced Workshop in Regulation and Competition, 20th Annual Western
Conference, June 2007.
∗
Correspondence to: James J. Murphy. Dept of Economics, Rasmuson Hall, 3211 Providence
Drive, Anchorage, AK 99508. Phone: 907-786-1936. Fax: 907-786-4115. Email:
jmurphy@cbpp.uaa.alaska.edu.
Imperfect Enforcement of Emissions Trading and Industry Welfare: A Laboratory
Investigation
Abstract: This paper uses laboratory experiments to investigate the performance of emission
permit markets when compliance is imperfectly enforced. In particular we examine deviations in
observed aggregate payoffs and expected penalties from those derived from a model of riskneutral payoff-maximizing firms. We find that the experimental emissions markets were
reasonably efficient at allocating individual emission control choices despite imperfect
enforcement and significant noncompliance. However, violations and expected penalties were
lower than predicted when these are predicted to be high, but were about the same as predicted
values when these values were predicted to be low. Thus, although a standard model of
compliance with emissions trading programs tends to predict significantly higher violations than
we observe when subjects have strong incentives to violate their emissions permits, individual
emissions control responsibilities are distributed among firms as predicted.
Keywords: enforcement, compliance, emissions trading, permit markets, pollution, laboratory
experiments
JEL Codes: C91, L51, Q58
1. Introduction
Much of what we understand about the advantages of emissions trading programs, particularly
vis-à-vis traditional command and control approaches, is based on models of full compliance
with these policies. However, emissions trading policies are not likely to perform as expected if
these programs are not enforced well. Recognizing this concern, there is now a significant body
of theoretical literature on the consequences of imperfect enforcement of emissions trading
programs (e.g. Keeler 1991, Malik 1990 and 1992, Stranlund and Dhanda 1999, Stranlund 2007).
While the theory of the compliance and enforcement problem in emissions trading has
advanced quite far, there are few empirical investigations of compliance behavior and the
performance of emissions markets under imperfect compliance. The dearth of empirical research
in this area is due to the fact that opportunities for empirical analyses of imperfect enforcement
1
in existing trading programs are limited. 1 In situations in which naturally occurring data are
limited, laboratory experiments are particularly valuable. In fact, several recent papers use
experiments to examine various aspects of imperfect compliance in emission trading programs
(Cason and Gangadharan 2006, Murphy and Stranlund 2006 and 2007). These works provide
valuable results about the compliance behavior of subjects in experimental emissions permit
markets, but none deal directly with the effects of noncompliance on the social costs and benefits
of these programs. 2 In this study, we use the data from a series of emissions trading experiments
to examine the impacts of imperfect enforcement on industry welfare. By imperfect enforcement
we mean that enforcement efforts—monitoring and penalties—are not sufficient to induce full
compliance by all firms.
The main value of competitive emissions permit markets is that they will produce the
allocation of emissions control among firms that maximizes industry profit, given the reduction
of aggregate emissions. Malik (1990) demonstrates that this result holds under reasonable
circumstances even when enforcement cannot induce full compliance. Moreover, he shows that
this result is independent of firms’ risk preferences. Since permit markets are predicted to
distribute control responsibilities efficiently, the main conceptual effect of imperfect
enforcement is that individual firms will violate their permits and therefore aggregate emissions
will exceed the number of permits that are put into circulation. When this occurs, it is easy to
demonstrate that trading will distribute permits such that the individual violation choices of risk-
1
For example, the EPA’s SO2 Allowance Trading Program and the NOX Budget Program have achieved such high
rates of compliance that there is simply not enough variation to conduct meaningful econometric analyses of
compliance decisions in these programs. See the most recent compliance reports for these programs, U.S. EPA
(2007a and 2007b).
2
Although experimental techniques have been used to evaluate other policy initiatives, including some aspects of
emissions trading programs (see the review by Muller and Mestelman 1998 and papers in the book edited by Isaac
and Holt 1999), these techniques have not yet been widely applied to issues of regulatory enforcement. By far, the
bulk of experimental analyses of compliance and enforcement is in the area of income tax compliance. See Alm and
McKee (1998) and Torgler (2002) for comprehensive surveys of this literature.
2
neutral firms will minimize aggregate expected penalties for the given level of emissions. Since
the distribution of individual emissions maximizes gross profit (penalties excluded) and the
distribution of individual violations minimizes expected penalties, a competitive emission
trading program that is imperfectly enforced will maximize aggregate expected net profits
(aggregate gross profits minus aggregate expected penalties), given the level of aggregate
emissions that is achieved.
Our laboratory experiments were designed to investigate whether and how aggregate
gross profit, aggregate expected penalties, and aggregate expected net profits deviate from
theoretical predictions that are based on risk-neutral profit-maximizing firms when enforcement
is not expected to induce their full compliance. Empirically, deviations from predictions about
industry welfare can be decomposed into two types of effects. The first are individual allocation
effects that account for deviations in aggregate profits and expected penalties from model
predictions, given the observed levels of aggregate emissions and aggregate violations. Isolating
these effects allows us to examine whether the market allocates individual emissions control
responsibilities among firms so as to maximize aggregate gross profit and allocates violations to
minimize aggregate expected penalties, even if observed aggregate emissions and violations
differ from predicted values. It is important to note that if the distribution of individual violations
does not maximize aggregate gross profits, then we will reject Malik’s assertion that emission
markets will distribute individual control responsibilities efficiently even when these markets are
imperfectly enforced. However, we cannot say that a permit market fails if we find that
individual violation choices do not minimize aggregate expected penalties. Deviations in
individual violations from predicted values that lead to higher expected penalties can be due to
differences in risk preferences (or other compliance-related preferences) that are assumed away
3
by the model of risk-neutral profit-maximizing behavior. The second part of deviations in gross
profits and expected penalties from predictions are aggregate compliance effects that can arise if
aggregate emissions and violations differ from predicted values. A difference between observed
and predicted aggregate emissions and violations also do not imply a permit market failure
because they can also stem from a failure of a standard model of firms to accurately predict
compliance choices.
The deviations in aggregate gross profits, expected penalties, and expected net profits
from model predictions, and our decompositions of these deviations into allocation and
compliance effects, yield several results. One of the most important is that the experimental
markets tended to allocate individual emissions control so that aggregate gross profits were very
close to maximized values, given the observed levels of aggregate emissions. Thus, we find
strong support for Malik’s hypothesis that emissions markets will distribute individual abatement
efforts efficiently despite imperfect enforcement and significant noncompliance.
However, aggregate violations were significantly lower than predicted when predicted
violations were very high, while the subjects’ violations were quite close to predicted values
when predicted violations were lower. In all cases, individual violation choices did not minimize
aggregate expected penalties at the observed levels of aggregate violations. However, because
the subjects did not violate their permits as much as predicted when their violations were
predicted to be high, aggregate expected penalties were significantly lower than predicted in
these treatments. In the treatments in which predicted violations were lower, aggregate expected
penalties were usually not statistically different from predicted values.
These results point to a failure of the model of risk-neutral profit-maximizing behavior to
accurately predict compliance behavior when the subjects had very strong incentives to violate
4
their permits. Despite this our observations of aggregate expected net profits—gross profits
minus expected penalties—were often not very far away from our predictions. Observed
aggregate expected net profits were at least 96% of their maximums for the treatments in which
we predicted low violations, and between 87% and 96% of maximums for the treatments for
which predicted violations were high.
With imperfectly enforced emissions trading programs the two most important items to
be concerned about are the aggregate level of emissions control and the distribution of individual
emissions control. Our results suggest that emissions trading is a reasonably efficient way to
allocate individual emissions control responsibilities, even when enforcement is imperfect.
Moreover, poorly enforced programs may not result in as much noncompliance as a standard
model would predict. Depending on the benefits of pollution control in a particular setting, it is
easy to imagine how lower-than-predicted violations and emissions could result in higher-thanpredicted social welfare if the additional benefit of pollution control outweighs the reduction in
the expected net profits of pollution sources. This, of course, is not a justification for designing
poorly enforced trading programs. Our analysis merely suggests that imperfect enforcement may
not always be as costly as standard models predict.
2. Firm behavior and market equilibrium under imperfectly enforced emission trading
In this section we present a standard model of firm behavior and the equilibrium of an
imperfectly enforced emissions trading policy that provides the foundation for our experimental
design. Because all of the results in this section can be gleaned from the existing literature (in
particular, Malik 1992, Stranlund and Dhanda 1999, and Stranlund 2007), we only sketch the
theory.
5
Consider a fixed set of heterogeneous risk neutral firms. Firm i’s gross profit from
emitting qi is given by the strictly concave gross profit function bi (qi ) . 3 Absent a regulatory
motivation to reduce its emissions, the firm emits qi , the solution to bi′(qi ) = 0 . A market for
emission permits will generate a permit price that motivates the firm to emit qi < qi . For these
levels of emissions, bi′(qi ) > 0 .
A total of L < ∑ qi emissions permits are distributed to the firms free of charge. Firm i’s
initial allocation is li0 , and it chooses to hold li permits after trading is completed. Each permit
confers the legal right to emit one unit. Assume competitive behavior in the permit market so
that all trades take place at a constant price p. The analysis throughout is static.
If a firm is noncompliant, then its emissions exceed the number of permits it holds and
the magnitude of its violation is vi = qi − li > 0 . If the firm is compliant, qi − li ≤ 0 and vi = 0. To
check for compliance, each firm is audited with a known and fixed probability π. A firm that is
found to be in violation is penalized according to a penalty function, f (vi ) , which is increasing
and strictly convex for vi ≥ 0 . The audit probability and the penalty function are exogenous and
do not vary across firms.
Assuming throughout that each firm chooses positive emissions and holds a positive
number of permits, firm i’s objective is:
max bi (qi ) − p (li − li0 ) − π f (qi − li )
qi ,li
subject to qi − li ≥ 0.
3
[1]
Strictly speaking, bi (qi ) is the firm’s gross profit assuming that it makes all of its input and output choices
optimally. See Montgomery (1972) for a demonstration of the concavity of profit in emissions for firms that are
price-takers in input and output markets. Many authors choose to model firms’ abatement costs rather than profits
from emissions. We presented our subjects with profit functions so we use them here to maintain consistency. There
is no loss of generality in our approach.
6
Restricting the firm to v i = qi − li ≥ 0 follows from the fact that a firm will never have an
incentive to be over-compliant. Letting L denote the Lagrange equation for [1] and λi denote
the multiplier attached to the constraint qi − li ≥ 0 , the first-order conditions for a solution to [1]
are:
Lq = bi′(qi ) − π f ′(qi − li ) + λi = 0;
[2]
Ll = − p + π f ′(qi − li ) − λi = 0;
[3]
Lλ = qi − li ≥ 0, λi ≥ 0, λi (qi − li ) = 0.
[4]
Because the constraint qi − li ≥ 0 is linear and the firm’s objective is strictly concave these
conditions are necessary and sufficient to identify unique optimal choices of emissions, permit
demand, and violation level.
As noted in the introduction, Malik (1990) demonstrated an interesting and important
result concerning the performance of emission trading programs and imperfect enforcement.
Under reasonable specifications of the probability of monitoring firms, which include random
monitoring as in this paper, a competitive permit market will distribute individual emissions
control responsibilities so that, regardless of the level of aggregate abatement actually achieved,
aggregate abatement costs are minimized. Moreover, Malik showed that this result does not
depend on the firms’ risk preferences. Malik’s result is fully equivalent to saying that aggregate
gross profit will be maximized given the actual level of aggregate emissions despite imperfect
enforcement and significant noncompliance.
To demonstrate this, combine equations [2] and [3] to obtain p = bi′(qi ) , which is the
familiar rule that competitive firms will choose their emissions to equate the going permit price
to their marginal benefits of increased emissions. Equating marginal gross profits across firms
7
gives us the necessary conditions for maximizing industry gross profit given some level of
aggregate emissions. Therefore, letting Q denote aggregate emissions, in a permit market
equilibrium we have:
n
p = B′(Q), where B (Q) = max ∑ bi (qi ) s.t.
qi
i =1
n
∑q
i =1
i
= Q.
[5]
Note that a firm’s emissions choice is independent of the enforcement strategy it faces,
and thus holds regardless of its compliance choice. Therefore, the ability of the permit market to
allocate individual emissions choices efficiently is not affected by the enforcement strategy that
is applied to the market or the risk preferences of firms. Testing this conclusion is one of the
primary motivations for our experiments.
Because competitive trading of a limited supply of permits is expected to distribute
individual emissions choices efficiently despite imperfect enforcement, the main theoretical
consequence of imperfect enforcement is that aggregate emissions will exceed the aggregate
supply of emissions permits. Toward characterizing the equilibrium violations of noncompliant
risk neutral firms, [3] indicates that a noncompliant firm chooses its violation to satisfy
p = π f ′(vi ) . Note that a firm’s violations depend on the permit price and the enforcement
strategy all firms face, but it does not depend on anything that is unique about the firm. 4 Since
the determinants of the firms’ violation choices are the same, if they are all noncompliant they all
choose the same level of violation. What drives this result is the ability of a permit market to
4
For this reason, Stranlund and Dhanda (1999) argued that a budget-constrained regulator that seeks to minimize the
aggregate violations of heterogeneous risk neutral firms cannot use differences in the firms’ control costs or initial
permit allocations to target its monitoring effort. The reason is that each firm’s emissions and violation decisions are
keyed to the permit price so that, at the margin, there are no differences among them that an enforcer can exploit.
Murphy and Stranlund (2007) use laboratory experiments to test and confirm the hypothesis that firms’ violations
choices are independent of their abatement costs. They do find, however, some evidence that violations may depend
in part on whether firms are net buyers or net sellers of permits.
8
equate the marginal incentives of risk-neutral firms to release emissions and to violate their
permits.
Just like equating the firms’ marginal incentives to pollute maximizes aggregate gross
profit given aggregate emissions, equating the marginal violation incentives of risk neutral firms
minimizes aggregate expected penalties given aggregate emissions. Given Q, and a supply of
permits L, aggregate violations are V = Q − L . Obviously we must have V ≥ 0. It is
straightforward to show that in a permit equilibrium,
n
p = P′(V ), where P (V ) = min ∑ π f (vi ) s.t.
vi
i =1
n
∑v
i =1
i
=V.
[6]
That is, P(V) is minimum aggregate expected penalties for aggregate violations V, and in
equilibrium the permit price is equal to the marginal of this function.
Having characterized the emissions and violation choices of risk neutral firms in a
competitive emissions trading program, as well as their aggregate gross profits and expected
penalties, let us now turn to the market equilibrium of such a program. Since the focus of this
paper is on the industry-level welfare consequences of imperfect enforcement and compliance,
we determine an equilibrium permit price and aggregate emissions, given an initial distribution
of L emissions permits and an enforcement strategy that cannot produce perfect compliance. Our
results in [5] and [6] reveal a three-way equality that uniquely identifies the equilibrium permit
price and aggregate emissions:
p = B′(Q) = P′(Q − L).
[7]
The equilibrium comparative statics of this problem are easy to demonstrate (see
Stranlund and Dhanda 1999). Aggregate emissions and violations are increasing as enforcement
is weakened, either by reducing the monitoring probability or reducing the marginal penalty
function. Because weaker enforcement decreases the aggregate demand for permits, the
9
equilibrium permit price falls. Increasing the supply of permits decreases the equilibrium permit
price and increases aggregate emissions, but aggregate violations fall.
In this paper, however, we focus on the deviations of behavior in the lab from the
predictions of the model described above. Moreover, since we are interested consequences of
these deviations on industry-level payoffs, we will focus on the aggregates that our experimental
markets produce— aggregate emissions, aggregate violations, aggregate gross profits, aggregate
expected penalties, and aggregate expected net profits. Denote our actual observations of these
values as Q a , V a , B a , P a , and W a , respectively. Given our experimental design, the theory
described above for risk-neutral profit-maximizing firms provides predictions for aggregate
emissions and violations, Q p and V p . Moreover, the theory predicts that the distribution of
individual emissions will maximize aggregate gross profits, and the distribution of individual
violations will minimize aggregate expected penalties. Thus, our prediction of aggregate gross
profits is B (Q p ) defined by [5], and our prediction of aggregate expected penalties is P (V p )
defined by [6]. Finally, it is easy to demonstrate that the predictions of individual emissions and
violations maximizes aggregate expected net profits, W (Q p ) = B (Q p ) − P (V p ) . (We write
expected net profits as a function of aggregate emissions alone because these automatically
determine aggregate violations given the supply of permits).
Empirically, observed deviations from model predictions can be decomposed into two
effects: individual allocation effects and aggregate compliance effects. Individual allocation
effects occur when individual emission and violation choices deviate from model predictions
given the observed level of aggregate emissions and violations. Aggregate compliance effects
arise whenever the observed level of aggregate emissions, and hence aggregate violations,
deviate from the predictions.
10
This decomposition of the deviations in observed and predicted aggregate gross profits is
B a − B (Q p ) = ⎡⎣ B a − B(Q a ) ⎤⎦ + ⎡⎣ B(Q a ) − B(Q p ) ⎤⎦ .
Allocation Effect
[8]
Compliance Effect
The individual allocation effect in [8] is the difference between observed and maximum
aggregate gross profits, conditioned on the observed level of aggregate emissions. Recall that
Malik (1992) showed that a competitive emissions permit market should allocate individual
emissions to maximize aggregate gross profit at the observed level of aggregate emissions,
regardless of firms’ preferences for risk. By definition, the allocation effect in [8] must be nonpositive, and if it is negative then the permit market has failed to distribute individual emissions
efficiently.
Note that the aggregate compliance effect of deviations from predicted aggregate gross
profits in [8] is conditioned on the assumption that the permit market distributes individual
emissions efficiently. This term can be any sign depending on whether observed aggregate
emissions ( Q a ) are greater than, less than, or equal to the theoretically predicted level, Q p . Note
that deviations in B (Q a ) and B(Q p ) do not indicate market failures because deviations of
Q a from Q p could be due to differences in compliance incentives from those of risk-neutral
profit-maximizing firms. Thus, if B (Q a ) and B (Q p ) differ, the failure is because the model
failed to predict aggregate emissions correctly.
In the same way we can decompose the deviation between observed and predicted
expected aggregate penalties:
P a − P (V p ) = ⎡⎣ P a − P (V a ) ⎤⎦ + ⎡⎣ P(V a ) − P(V p ) ⎤⎦ .
Allocation Effect
Compliance Effect
11
[9]
The allocation effect in this case is the difference between observed and minimum expected
aggregate penalties, conditioned on observed aggregate violations. This term is non-negative,
because P(V a ) is minimum aggregate expected penalties given observed aggregate emissions
Q a , and hence, observed aggregate violations V a . Again, deviations in observed and predicted
expected penalties are not market failures. They indicate instead a failure of the model of riskneutral profit-maximizing firms to correctly predict individual violations. The compliance effect
is conditioned on the firms choosing violations that minimize aggregate expected penalties, but
will differ from zero if observed and predicted aggregate violations differ.
Finally, the allocation and compliance effects of deviations in aggregate expected net
profits is
W a − W (Q p ) = ⎡⎣W a − W (Q a ) ⎤⎦ + ⎡⎣W (Q a ) − W (Q p ) ⎤⎦ .
Allocation Effect
[10]
Compliance Effect
The allocation effect on expected net profit is simply the allocation effect on gross profits in [8]
minus the allocation effect on expected penalties in [9]. The compliance effect in [10] is defined
in the same way.
3. Experimental Design and Procedures
3.1 Experiment design
Our experiments were designed to compare laboratory behavior to the predictions generated
from the theory just described, but the subjects were placed in a more neutral environment. To
avoid introducing potential biases due to individual attitudes about the environment or emissions
trading, we framed the experiments as a production decision in which permits conveyed a license
to produce, rather than an emissions decision. We also avoided the term “profit”, choosing
12
instead the more neutral term “benefit”. (Throughout the paper, however, we use profits and
emissions). We are mainly interested in whether aggregate gross profits, expected penalties and
expected net profits differ from predicted values, and if so, the extent to which these deviations
are due to the inability of a permit market to allocate individual emissions choices efficiently or
to compliance choices by the subjects that differ from those of a profit-maximizing risk neutral
individual. <INSERT TABLE 1>.
Table 1 summarizes the experimental design. During each period, subjects
simultaneously chose to emit units of an unspecified pollutant and traded in a market for permits
that conveyed the right to emit. In the nine Imperfect Enforcement treatments, subjects could
emit as much as they wished (up to a capacity constraint) regardless of the number of permits, l,
they owned. However, at the end of the period, each individual was audited with a known,
exogenous probability. If an individual was audited and found to be non-compliant (i.e., total
emissions exceeded permit holdings), then a penalty was applied. In the two Perfect Enforcement
treatments, subjects were only able to trade in the permit market; emissions were automatically
set equal to the final permit balance. Because there was no compliance choice in these two
baseline treatments, there was, of course, no need for fines or audits.
Subjects received a gross profit from their choice of emissions, q, which was generated
from a linear marginal gross profit function, b′ (q ) = 18 − θ q . Each experiment had eight subjects
divided evenly into two types; subjects were randomly assigned a type. Subjects with a high
marginal gross profit function ( θ H = 1 ) also had a greater emission capacity of 17 units. Subjects
with a low marginal gross profit function ( θ L = 2 ) could emit up to 8 units. Emissions were
constrained to be a whole number.
13
Limiting the total supply of permits imposed an aggregate emissions standard, L. We
consider two aggregate standards. In the experiments with a low aggregate standard ( LL = 28 ),
denoted Low Standard, each of the four high marginal gross profit subjects was initially
allocated l 0 = 3 permits, and the four low marginal gross profit subjects were each given four
permits. In the high aggregate standard experiments ( LH = 56 ), denoted High Standard, there
were two different initial allocations of permits. With the Uniform initial allocation, each of the
eight subjects started with seven permits. With the Non-uniform initial allocation, the high
marginal gross profit subjects began with l 0 = 13 permits, and the low marginal gross profit
subjects had a single permit.
The treatment variables were the probability of an audit and the marginal penalty
function (which together define an enforcement strategy), the initial permit allocation, and the
total supply of permits. Each of the eleven treatments was repeated three times. In the Imperfect
Enforcement treatments, each subject’s record was examined with a known probability π. If a
subject was found to be non-compliant, that is q > l, then she was assessed a penalty that was
generated from a linearly increasing marginal penalty function, f ′(q − l ) = F + φ (q − l ). By
changing the parameters of the expected marginal penalty function, π f ′(q − l ) = π [ F + φ (q − l )],
we developed three enforcement strategies, which we label Medium(πH), Medium(πL), and Low.
In theory, all risk neutral subjects should choose to be noncompliant under each of these levels of
enforcement. The treatments Medium(πH) and Medium(πL) involved the same expected marginal
penalties, but Medium(πH) had a higher monitoring probability and a relatively low marginal
penalty function (πH = 0.70, F = 6, φ = 1.43), whereas Medium(πL) had a lower monitoring
probability and a higher marginal penalty function (πL = 0.35, F = 12, φ = 2.90). Our intention
here was to examine whether the subjects reacted differently to monitoring and penalties. The
14
Low marginal expected penalty treatments had the weakest enforcement strategy with the low
monitoring probability and a low marginal penalty function (πL = 0.35, F = 2, φ = 2.90).
Enforcement parameter values were chosen, in part, so that the expected marginal penalty
functions are parallel to each other—each has a slope of about one.
3.2 Experiment procedures
Participants were recruited from the student population at the University of Massachusetts,
Amherst. Subjects were paid $7 for agreeing to participate and showing up on time, and were
then given an opportunity to earn additional money in the experiment. These additional earnings
ranged between $5.68 and $17.49, with a mean of $13.67 (σ = 1.46). Earnings were paid in cash
at the end of each experiment. Each experiment lasted about 2 hours.
The experiments were run in a computer lab using software designed specifically for this
research. To familiarize subjects with the experiments, we ran a series of training experiments.
In the first stage of the trainers, students read online instructions that included interactive
questions to ensure that they understood the instructions before proceeding. After everyone had
completed the instructions and all questions were answered, the training experiment began.
These practice rounds contained all the same features as the “real data” experiments with the
exception that we used a different set of parameters. The data from the trainers were discarded.
We recruited participants from the pool of trained subjects for the real data sessions.
Subjects were allowed to participate in multiple sessions. A total of 176 subjects
participated in 33 eight-person market experiments (11 treatments, three groups per treatment).
Because subjects were allowed to participate in multiple sessions, the number of unique
participants is less than the total required. Prior to the start of the real data experiments, subjects
15
were given a summary of the experiment instructions. 5 The experimenter read these instructions
aloud and answered any questions. Each subject was given a calculator, a pencil and paper.
Each experiment consisted of 12 identical rounds. At the start of each period, the eight subjects
were each given an initial allocation of permits and $10 in experimental cash.
A unique feature of our experiments is that the emission decisions and permit market
trading were unbundled into two separate, but simultaneous, activities. We did this to allow for
the possibility that the emission levels and permit holdings could differ, thereby introducing a
compliance decision. During the period and concurrent with the production decision, subjects
were able to alter their permit holdings by trading in a continuous double auction. In the auction,
individuals could submit bids to buy or asks to sell a single permit. The highest bid and lowest
ask price were displayed on the screen. A trade occurred whenever a buyer accepted the current
ask or a seller accepted the current bid. After each trade, the current bid and ask were cleared
and the market opened for a new set of bids and asks. The trading price history was displayed on
the screen.
Each period lasted a total of five minutes. The permit market was open for the entire
period, but production had to be completed in the first four minutes. The one-minute
reconciliation period gave subjects a final opportunity to adjust their permit holdings. After each
period ended, random audits were conducted and penalties were assessed. All information
relating to audit outcomes was private.
5
The complete instructions, along with a summary are available online at
http://faculty.cbpp.uaa.alaska.edu/jmurphy/research.html.
16
4. Results
In this section we analyze the data from our experiments to investigate the effects of imperfect
enforcement on aggregate gross profits, expected penalties and expected net profits. We are
particularly interested in how our observations of these values differ from the predictions of the
theoretical model of section. Our data is made up of 11 treatments (indexed by k), each of which
was played by three groups (indexed by j) over 12 rounds (indexed by t). We are interested only
in aggregate outcomes, not individual choices. The first two periods are omitted from the
analysis to minimize the effects of learning, leaving 10 observations per group. (Omitting the
first two rounds does not change any of our qualitative results). Therefore, we have 330 grouplevel observations (11 treatments, 3 groups per treatment, 10 rounds per group).
4.2 The compliance and allocation effects of deviations from predicted gross profits
We begin our analysis with the comparisons of aggregate emissions and violations (Table 2). For
each treatment k, we compare the mean of observed aggregate emissions and violations
(averaged over the 3 groups and 10 rounds of the treatment), denoted Q a and V a , to the
predictions, Q p and V p , from the model of section 2. For the Imperfect Enforcement treatments,
note that mean aggregate violations, V a , follow the basic comparative static predictions of the
model: violations tend to increase with weaker enforcement (given an aggregate standard, the
Low enforcement strategy treatment has the most violations) and lower aggregate standard (given
an enforcement strategy, violations are higher under the Low Standard).
The last column of Table 2 presents the differences between mean and predicted
aggregate violations. Since each treatment has a fixed supply of permits, this difference in
aggregate violations is identical to the difference in aggregate emissions; that is,
17
V a − V p ≡ Q a − Q p . To investigate the statistical significance of these differences we employ
the following mixed effects linear regression:
8
Vkjta − Vkp = α + ∑ β k X kjt + ν j + ε kjt ,
[12]
k =1
where X is the set of dummy variables for eight of the nine imperfect compliance treatments,
with Low Standard, Medium (πH) Enforcement as the omitted dummy variable. 6 For the Perfect
Enforcement treatments, predicted and mean aggregate violations (and aggregate emissions) are
zero by design and are therefore not included in the regression model.
The most important results from Table 2 will have impacts throughout the analysis: the
differences between mean and predicted aggregate violations, V a − V p , are negative and
statistically significant for the three Low Standard treatments, but are statistically
indistinguishable from zero for the six High Standard treatments. This suggests that individual
choose lower-than-predicted violations when they are predicted to choose high violations, but
that there violations are close to predicted values when these predictions are low. Clearly, the
standard theoretical model of compliance in emissions trading programs does not accurately
predict aggregate violations when enforcement is very weak. <INSERT TABLE 2>
4.2 The compliance and allocation effects of deviations from predicted gross profits
We now turn to analyzing aggregate gross profits using the results shown in Table 3. If the
emissions permit market is perfectly competitive and all firms are profit maximizers, then for
each treatment, the predicted aggregate gross profit is B (Q p ) from [5]. That is, B (Q p ) is
χ 2 test of the null hypothesis that α + β k = 0 , or in
the case of the omitted dummy variable, Low Standard, Medium (πH) Enforcement, α = 0 .
6
For each treatment k, Table 2 reports the results of a Wald
18
maximum aggregate gross profit achievable given predicted aggregate emissions Q p . For each
treatment, the average (over groups and rounds) of observed aggregate gross profits is denoted
B a . In order to decompose the difference between observed and predicted aggregate gross
profits into allocation and compliance effects, we calculated the maximum possible gross profit
given the observations of aggregate emissions for each group, round, and treatment. In Table 3
we report the means of these values for each treatment, B (Q a ) . <INSERT TABLE 3>
The results in the B a − B (Q p ) column of Table 3 show that observed aggregate gross
profits are essentially equal to predicted gross profits under the Perfect Enforcement treatments.
This simply replicates the well-known result that standard double auctions with perfect
compliance yield highly efficient outcomes. However, under the Imperfect Enforcement/Low
Standard treatments, observed gross profits are significantly lower than predicted gross profits.
Under the Imperfect Enforcement/High Standard treatments, the deviations of mean observed
gross profits from predictions are not statistically different for all but two of six cases. In
percentage terms, B a B(Q p ) , observed gross profits are always more than 97% of predicted
gross profits under the Imperfect Enforcement/High Standard, while they range from only 80%
to 94% of predicted gross profits under the Imperfect Enforcement/Low Standard treatments.
But recall that a deviation of observed gross profits from the predicted value does not
necessarily indicate that the permit market fails to distribute individual emission control
efficiently. Such a deviation could be due differences in observed and predicted aggregate
emissions that come from differences between actual and risk-neutral profit maximizing
compliance choices. To better explain the differences between observed and predicted gross
profits, we decomposed these differences into the allocation and compliance effects in equation
19
[8] for each group in each round and present the means of these values for each treatment in
Table 3.
The allocation effects in Table 3 provide a direct test of Malik’s (1990) hypothesis that
permit markets will allocate individual emissions efficiently despite imperfect enforcement. If
this hypothesis were to hold, then all the allocation effects in Table 3 would be statistically
indistinguishable from zero; clearly they are not. Note that the allocation effects are essentially
zero in our Perfect Enforcement treatments. Thus, when we did not give the subjects the
opportunity to violate their permits, they successfully allocated emissions among themselves to
maximize aggregate gross profits. However, the allocation effects are statistically significant in
all nine Imperfect Enforcement treatments. From a practical perspective, however, these effects
are very small and not economically significant since mean observed aggregate gross profits,
B a , are always at least 96% of the maximum possible value given the observed level of
emissions, B(Q a ) . We therefore conclude that the permit markets allocated individual emissions
choices efficiently, despite imperfect enforcement, significant noncompliance, and emissions and
violation choices that sometimes differ from their predicted values.
In light of the previous discussion about the differences between observed and predicted
aggregate violations (the results in Table 2), the compliance effects in Table 3 are not surprising.
By design, the individual compliance effect is exactly zero in our Perfect Enforcement
treatments. For the Imperfect Enforcement treatments, the compliance effects are negative and
significant only for the Low Standard treatments; these effects are statistically indistinguishable
from zero in all of the High Standard treatments. These results are simply a translation into
aggregate gross profits of the result that actual violations are significantly lower than predicted
for the Low Standard treatments but are essentially zero in the High Standard treatments.
20
The large compliance effects for the Imperfect Enforcement/Low Standard treatments is
the reason that mean observed gross profits are significantly lower than predicted in these
treatments. That is, the permit markets were reasonably efficient at allocating individual
emissions, but the subjects chose significantly lower-than-predicted violations. Mean observed
gross profits are very close to predicted values for the Imperfect Enforcement/High Standard
treatments because the allocations effects are small and the compliance effects are
indistinguishable from zero. Again, the markets were reasonably efficient, but in these treatments
aggregate violations were essentially the same as predicted.
4.3 The compliance and allocation effects of deviations from predicted expected penalties
We now examine deviations in observed expected penalties from predicted values and
decompose these deviations into allocation and compliance effects. The results are in Table 4. If
the subjects are risk-neutral profit-maximizers, then for each treatment, the predicted aggregate
expected penalties are P (V p ) from [6]. That is, P (V p ) is minimum aggregate expected
penalties given predicted aggregate emissions V p .
The means of observed expected penalties for each treatment, denoted P a , are calculated
as follows. For each individual in each round of the experiments, we calculated the penalty that
she would incur if audited for her actual level of violations; this was then multiplied by the audit
probability to get her expected penalty. These values were then summed over the individuals in a
group in each round to obtain aggregate expected penalties for each group in each round. In
Table 4 we present the means of these values (averaged over groups and rounds) for each
treatment. Note that these are the averages of aggregate expected penalties, not the means of the
penalties that were actually imposed as a result of the random audits. This is the appropriate
21
metric as we are interested in the choices that were made given the ex ante expected penalties,
not the ex post realizations. Obviously these values are equal to zero in the Perfect Enforcement
treatments. It is also important to recall that differences between P a and P (V p ) do not indicate
permit market failures; they are due instead to differences in compliance choices from those of
risk-neutral, profit-maximizing agents. Finally, to calculate the allocation and compliance effects
of the differences between observed and predicted expected penalties, we calculated the
minimum possible aggregate expected penalty given the observed aggregate violations for each
group, round, and treatment. In Table 4 we report the means of these values for each treatment,
P(V a ) . <INSERT TABLE 4>
Note that mean observed expected penalties are significantly lower than predicted for the
three Imperfect Enforcement/ Low Standard treatments. In contrast, mean expected penalties are
higher that predicted for the Imperfect Enforcement/ High Standard treatments, but the
differences are statistically significant in only two of six cases. Note, however, that the
allocations effects are always positive and significant (although weakly significant in one case).
This indicates that, given the observed levels of aggregate violations, individual violations were
not distributed in the way that would minimize aggregate expected penalties. The compliance
effects are negative and significant for the Imperfect Enforcement/ Low Standard treatments
while they are not different from zero in the Imperfect Enforcement/ High Standard treatments.
These simply reflect that facts that the subjects chose significantly lower-than-predicted
violations in the Imperfect Enforcement/ Low Standard treatments, while aggregate violations
were very close to predicted values under the Imperfect Enforcement/ High Standard treatments.
22
4.4 The compliance and allocation effects of deviations from predicted expected net profits
In this final section, we pull together our results about deviations in aggregate gross profits and
expected penalties from predicted values to answer the basic question of how well the groups in
our experiments performed relative to predictions. That is, we examine deviations in aggregate
expected net profits (gross profits minus expected penalties) from predictions.
In Table 5 we first present predicted net profits, W (Q p ) = B(Q p ) − P(V p ) . Recall that
W (Q p ) is maximized expected net profit: the predicted levels of aggregate emissions and
resulting aggregate violations, as well as the levels of individual emissions and violations,
maximize the expected aggregate payoff to the industry. We also present mean observed
expected net profits, W a = B a − P a , and mean maximized expected net profits at the observed
levels of aggregate emissions, W (Q a ) = B (Q a ) − P (V a ) . Note that the differences between
predicted and mean observed expected net profits, W a − W (Q p ) , is negative and significant for
each treatment. However, they are very close to their maximized values. In percentage terms,
observed expected net profits are very nearly 100% of maxima for the Perfect Compliance
Treatments; they exceed 95.8% of maxima for each of the Imperfect Enforcement/ High
Standard treatments; they are somewhat lower for the Imperfect Enforcement/ Low Standard
treatments, ranging from 87% to 96% of maximized expected net profits.
Mean observed expected net profits deviate from maximized values by greater amounts
(in percentage terms) under the Imperfect Enforcement/ Low Standard treatments because of the
significant compliance effects in these treatments. Although the allocation effects for all
Imperfect Enforcement treatments are significant, they are similar in magnitudes across the Low
Standard and High Standard treatments. However, the compliance effects in the Imperfect
Enforcement/ Low Standard treatments are large and significant, while they are very small and
23
insignificant in the Imperfect Enforcement/ High Standard treatments. The groups under the
Imperfect Enforcement/ Low Standard treatments tended to do worse mainly because they chose
significantly lower-than-predicted violations.
5. Conclusion
The most important results of our work are that experimental emissions permit markets are
highly efficient at allocating individual emissions control, despite imperfect enforcement and
significant violations, but aggregate violations may not be as high as one would predict with a
standard model of behavior, particularly when the model predicts high levels of noncompliance.
In treatments in which subjects did not violate their permits as much as predicted, mean
aggregate expected payoffs were lower than maximized expected payoffs. It is important to
reiterate that this finding does not imply some sort of inefficiency. Rather it appears to be due
mainly to violation choices that differ from those that a risk-neutral payoff-maximizing
individual would make. If there is a failure, it is a failure of the standard model to accurately
predict compliance choices, not a failure of permit markets to allocate emissions efficiently.
In fact, lower-than-predicted violation choices can mean higher social welfare. We have
focused our analysis on the welfare of firms operating under imperfectly enforced emissions
trading, but presumably there are damages from their emissions. We have not said anything
about pollution damage, because including it in our analysis can only be done in an ad hoc
manner. Nevertheless, when violations are lower-than-predicted, pollution damage is lower-thanpredicted. It is easy to come up with specifications of damage functions for our experiments with
which the lower-than-predicted violations we observe lead to higher-than-predicted social
welfare.
24
One should be careful about this possibility. It does not mean that imperfect enforcement
of emissions trading programs is somehow desirable; it only means that imperfect enforcement
may in some situations be less costly than standard models would predict. Recent theoretical
developments suggest that it is likely to be efficient to design tradable rights programs that
achieve perfect compliance (Stranlund 2007). Moreover, several current emissions trading
schemes have achieved perfect, or at least near perfect, compliance (e.g. the EPA’s SO2 and NOX
Budget trading programs). Our analysis does not address these situations. Instead, our analysis is
motivated by the fact that implementing emissions trading policies beyond their current
applications will often mean moving them into contexts in which inducing and maintaining
perfect compliance will be more difficult. With the continuing application of market-based
policies into new regulatory settings, it is virtually certain that regulators will have to confront
the problems associated with imperfect enforcement, if they have not had to do so already. Our
analysis provides valuable information about the likely welfare effects of failing to induce
perfect compliance with tradable property rights regulations.
25
References
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Malik, A. S. 1990. “Markets for Pollution Control when Firms are Noncompliant.” Journal of
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Malik, A. S. 1992. “Enforcement Cost and the Choice of Policy Instruments for Controlling
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Muller, R.A. and S. Mestelman. 1998. “What Have We Learned from Emissions Trading
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Murphy, J. J. and J. K. Stranlund. 2007. “A Laboratory Investigation of Compliance Behavior
under Tradable Emissions Rights: Implications for Targeted Enforcement.” Journal of
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Transferable Emissions Permit System.” Journal of Environmental Economics and
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Torgler, B. 2002. “Speaking to Theorists and Searching for Facts: Tax Morale and Tax
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26
Table 1. Experimental Design
Enforcement
(none)
Aggregate Standard / Initial Allocation
Perfect Enforcement Treatments
Low Standard/ Uniform
High Standard/ Uniform
Imperfect Enforcement Treatments
Medium(πH)
Low Standard /Uniform
High Standard/ Uniform
High Standard / Non-uniform
Medium(πL)
Low Standard / Uniform
High Standard / Uniform
High Standard /Non-uniform
Low
Low Standard / Uniform
High Standard Uniform
High Standard / Non-uniform
Each treatment was repeated three times with eight participants per group.
27
Table 2. Predicted and Actual Aggregate Emissions and Violations
Treatment
Qp
Qa
Vp
Va
V a −V p
28
52
52
64
28.0
48.4
40.4
55.7
0
24
24
36
20.4
12.4
27.7
–3.6***
–11.6***
–8.3***
56.0
63.5
65.4
76.3
0
8
8
20
7.5
8.9
20.3
– 0.5
0.9
0.3
Low Standard
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
High Standard Uniform Allocation
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
56
64
64
76
High Standard Non–uniform Allocation
Perfect Enforcement
64
63.9
8
7.9
– 0.1
Medium (πH)
64
65.4
8
9.4
1.4
Medium (πL)
76
74.5
20
18.5
–1.5
Low
Significance levels * p < 0.10, ** p < 0.05; *** p < 0.01, are for tests of
the null hypothesis that the value is equal to zero. Wald χ 2 tests are
obtained from a linear regression of V a − V p with dummy variables for
each treatment as the fixed effects and allowing for random effects
across groups and periods.
28
3. The Compliance and Allocation Effects of Deviations from Predicted Gross Profits
Allocation
Effect
Treatment
Percent Allocation Compliance
Efficiency
Effect
B (Q p )
B aQ
B(Q a )
B a − B(Q p )
B a B(Q p )
B a − B(Q a )
420
676
676
768
417.1
634.1
542.5
692.8
420.0
642.4
560.9
705.3
–2.9
–41.9***
–133.5***
–75.2***
99.3%
93.8%
80.2%
90.2%
–2.9
–8.3***
–18.5***
–12.5***
99.3%
98.7%
96.7%
98.2%
0
–33.6***
–115.1***
–62.7***
706.6
758.3
766.9
823.8
708.0
763.6
772.7
836.2
–1.4*
–9.7
–1.1
–12.2
99.8%
98.7%
99.9%
98.5%
–1.4*
–5.3**
–5.8**
–12.4***
99.8%
99.3%
99.3%
98.5%
0
–4.4
4.7
0.2
766.0
776.1
827.5
–17.0**
0.4
–19.1**
97.8%
100.0%
97.7%
–15.0***
–7.7***
–10.6***
98.1%
99.0%
98.7%
–2.0
8.1
–8.5
B a / B(Q a )
B (Q a ) − B(Q p )
Low Standard
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
High Standard Uniform Allocation
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
708
768
768
836
High Standard Non–uniform Allocation
Medium (πH)
Medium (πL)
Low
768
768
836
751.0
768.4
816.9
Significance levels * p < 0.10, ** p < 0.05, and *** p < 0.01, are for tests of the null hypothesis that the value is equal to zero.
Wald χ 2 tests are obtained from linear regressions of each variable with dummies for each treatment as the fixed effects for
treatment and allowing for random effects across group and period.
29
4. The Compliance and Allocation Effects of Deviations from Predicted Expected Penalties
Treatment
P(V p )
Pa
P(V a )
P a − P(V p ) P a P(V p )
Allocation
Effect
Compliance
Effect
P a − P(V a )
P (V a ) − P (V p )
Low Standard
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
0
148.9
149.5
126.7
0
129.0
81.1
94.9
0
123.2
70.4
83.9
– 19.9***
– 68.4***
– 31.8***
86.6%
54.3%
74.9%
5.8***
10.8**
11.1***
– 25.7***
– 79.4***
– 42.8***
0
45.1
55.5
71.4
0
40.2
48.1
51.9
3.5
13.8
20.9**
108.5%
133.0%
141.3%
5.0*
7.4**
19.6***
– 1.4
6.4
1.3
48.0
68.3
62.8
41.9
51.1
45.5
6.4
26.5**
12.2
115.3%
163.6%
124.2%
6.1**
17.1***
17.3**
0.4
9.4
– 5.1
High Standard Uniform Allocation
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
0
41.6
41.7
50.5
High Standard Non-uniform Allocation
Medium (πH)
Medium (πL)
Low
41.6
41.7
50.5
Significance levels * p < 0.10, ** p < 0.05; *** p < 0.01, are for tests of the null hypothesis that the value is
equal to zero. Wald χ 2 tests are obtained from a linear regression with dummy variables for each treatment as
the fixed effects and allowing for random effects across groups and periods.
5. The Compliance and Allocation Effects of Deviations from Predicted Expected Net Profits
Allocation
Effect
Treatment
W (Q a ) W a − W (Q p ) W a W (Q p )
Compliance
Effect
W a − W (Q a ) W (Q a ) − W (Q p )
W (Q p )
Wa
420.0
527.2
526.5
641.3
417.1
505.1
461.3
597.8
420.0
519.2
490.6
621.4
– 2.9*
– 22.0***
– 65.1***
– 43.5***
99.3%
95.8%
87.6%
93.2%
– 2.9*
– 14.1***
– 29.2***
– 23.6***
0
– 7.9***
– 35.9***
– 19.9***
706.6
713.2
711.4
752.4
708.0
723.5
724.6
784.3
– 1.4***
– 13.2***
– 14.9***
– 33.1***
99.8%
98.2%
98.0%
95.8%
– 1.4**
– 10.3**
– 13.2***
– 32.0***
0
– 2.9
– 1.7
– 1.2
724.1
725.0
782.1
– 23.4***
– 26.1***
– 31.3***
96.8%
96.4%
96.0%
– 21.1***
– 24.8***
– 27.9***
– 2.3
– 1.3
– 3.4
Low Standard
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
High Standard Uniform Allocation
Perfect Enforcement
Medium (πH)
Medium (πL)
Low
708.0
726.4
726.3
785.5
High Standard Non-uniform Allocation
Medium (πH)
Medium (πL)
Low
726.4
726.3
785.5
703.0
700.2
754.1
Significance levels *p < 0.10, ** p < 0.05; *** p < 0.01, are for tests of the null hypothesis that the value is
equal to zero. Wald χ 2 tests are obtained from a linear regression with dummy variables for each treatment as
the fixed effects and allowing for random effects across groups and periods.
1